So this is a bit of a necrobump but I ran into this issue and I've fixed it. The problem is that your network manager is spawning two player prefabs - meaning two instances of the LeapHandController object are active in the scene at once. Disable all leap objects in the hierarchy of the prefab, then enable them after you've confirmed that the prefab in question is the local player. If you ever have two LeapHandController GameObjects active in the scene, the tracking locks up and stops, even if you delete the subsequent objects afterwards.
Edit: I seem to have only fixed a part of the problem. I'm doing a deeper dive into networked hands, will update soon with more info.
Second Update: Got everything working. Tutorial should be incoming soon.